New York City Mayor Bill de Blasio holds a news conference at the New York City Office of Emergency Management in Brooklyn on Monday, July 20, 2015. Photo Credit: Charles Eckert

Mayor Bill de Blasio rebuffed a call Monday by Uber for a public sit-down on New York City's proposal to temporarily cap for-hire vehicles -- curbing the growth of the popular, app-dispatched livery service.

"I do not debate with the heads of private companies over their own self-interest," de Blasio said.

An Uber official sent an open letter earlier in the day challenging the mayor's contention that the legislation -- which the City Council may vote on as early as Thursday -- was about reducing congestion.

"If you have new concerns, we want to discuss them, face-to-face, and invite you to do so in a live-streamed conversation so all New Yorkers can watch," wrote Josh Mohrer, director of Uber's New York office.

City lawmakers are floating two bills to restrict livery companies based on their size while conducting a yearlong environmental review. Uber, with 26,000 vehicles in the city, including thousands used part time for livery work, would be the hardest-hit. Its growth would be limited to 200 additional cars in the next year.

About 80 supporters of the legislation, including Councilman Ydanis Rodriguez (D-Manhattan) and taxicab drivers who held placards displaying the number of years they've been working, rallied Monday outside City Hall.

"We are here to say this fight is not about donations. It is about the workers," said Bhairavi Desai, executive director of the Taxi Workers Alliance. "They want to attack the right of working people to exist in this industry."

A competitor, San Francisco-based Lyft, also came out against a cap Monday, though from a slightly different angle.

"The one clear result of freezing the market in place is a blow to competition and an artificial lock in for Uber and taxi industry market positions, primarily hurting outer borough passengers and drivers," Lyft director of public affairs David Mack said.